Math Journal

In my math group students often use their journals to work through and show math solutions. I base many of the problems we use on  Cognitively Guided Instruction (CGI) . CGI is a process developed by Elizabeth Fennema, Thomas Carpenter, Penelope Peterson, and Megan Franke and outlined in their book Children's Mathematics: Cognitively Guided Instruction.

It works to build on the math knowledge that students have. A part of the process is for students to solve a variety of types of problems using strategies that make sense to them: modeling and manipulatives, counting strategies, and combining numbers in different ways. Students work to communicate these strategies in their journals. We then share strategies together, so students can learn from their classmates’ process. 

I often work to use the students' names in the problems we solve. That adds to their enjoyment of the process. For some the problems are challenging, and they work hard to come up with their solutions and record them. Other times students easily come up with answers in their heads. Then the challenge is to understand the process they used and represent it in their journals.

This Year's Birthday Graph

Yikes! Is it really near the end of October?

Here is this year's class birthday graph. We do this early every school year. First we line up the names of the months along the carpet. Then the students line up behind their birthday months. We make observations such as which months have the greatest number of birthdays and the least. Then each student colors in a birthday cake and glues it above the correct month on a piece of posterboard. Here is the result.

Measurement Explorations

We have been working on finding items in the classroom that are about as long as the white cuisinaire rod. Once students each found 5 items (everything from a rainbow cube to a pet rat’s ear), we learned that the white rod is one centimeter long. Another day we did the same activity using inch cubes.

After these explorations, students had to measure some things at home with rulers or yardsticks for homework. Where possible they were to measure in English and metric units. As we shared the results of their measurements, we developed a clearer sense of the relationship between an inch and a centimeter. We completed charts in our journals where we estimated and then measured parts of our bodies, such as length of hand, length of foot, and circumference of head. We have continued our measurement explorations by beginning to talk about the concept of area and perimeter, applying the idea to items such as our classroom bench and rug.

Exploring Probability with Dreidels

In December we did a probability study with dreidels. We talked about the tops used for the traditional Hanukkah game of dreidel and what we would expect with a fair dreidel. Students said that each of the four sides should have an equal chance of coming up. One student calculated that if you spun a dreidel 100 times, it should land on each letter about 25 times.

In our study we compared plastic and wooden dreidels to see if one kind was more consistently fair than the other. Students spun the dreidels in class and at home for homework. In the hectic times leading up to Winter Break, we did not get all of our data entered into our spreadsheets. In January each student recorded results in spreadsheets on a classroom computer. We then viewed the results in a pie chart and as a bar graph. We speculated about why one side might come up more often than the others. Students thought about how they were made, about whether the letters were painted on or were on the side in relief, and about how the dreidel behaves when it is spun. I shared that to get an accurate picture we needed to have a lot of spins. We ended up with about 700 spins on plastic dreidels and over 900 with wooden dreidels. Here are our results: